A New Class of Combinatorial Markets with Covering Constraints: Algorithms and Applications

TL;DR

This paper introduces a novel combinatorial market model with covering constraints, providing existence proofs and polynomial algorithms for equilibria, applicable to scheduling, cloud computing, and networks, with unique solution set properties.

Contribution

It presents the first polynomial-time algorithm for equilibrium in a new market model with complex solution structures and demonstrates its fairness properties.

Findings

Existence of equilibrium proven using LP duality and submodular minimization.

Polynomial-time algorithm developed for finding market equilibrium.

Equilibrium set can be connected but non-convex, a novel phenomenon.

Abstract

We introduce a new class of combinatorial markets in which agents have covering constraints over resources required and are interested in delay minimization. Our market model is applicable to several settings including scheduling, cloud computing, and communicating over a network. This model is quite different from the traditional models, to the extent that neither do the classical equilibrium existence results seem to apply to it nor do any of the efficient algorithmic techniques developed to compute equilibria seem to apply directly. We give a proof of existence of equilibrium and a polynomial time algorithm for finding one, drawing heavily on techniques from LP duality and submodular minimization. We observe that in our market model, the set of equilibrium prices could be a connected, non-convex set. To the best of our knowledge, this is the first natural example of the phenomenon where the set of solutions could have such complicated structure, yet there is a combinatorial polynomial time algorithm to find one. Finally, we show that our model inherits many of the fairness properties of traditional equilibrium models.